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$\mathscr{E} = 1- \left( \dfrac{2}{a-2} - \dfrac{2}{a+2} \right) \left( a-\dfrac{3a+2}{4} \right)$

Let $a = 2016$. If $\mathscr{E}$ can be expressed in the form $\dfrac{x}{y}$, where $x$ and $y$ are coprime positive integers, find $x+y$.

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